The Bearsden home of the former Celtic manager was entered on Wednesday morning.
Rodgers' impact has already been welcomed by the Leicester squad, with the 46-year-old lifting the mood at their Belvoir Drive training ground.
The Northern Irishman infuriated the Bhoys support by abandoning the club late in the season, with an unprecedented third consecutive domestic treble still to play for.
The East Dunbartonshire property of Rodgers was broken into, but no-one was injured during the incident.
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Rodgers led Celtic to seven trophies, most recently winning Scottish Premiership, Scottish Cup and Scottish League Cup crowns in 2017 and 2018.
In the first game following his exit - a 2-1 win over Hearts - Celtic fans unveiled a banner which summed up their disappointment and anger towards him. "Never a Celt. Always a fraud".
Rodgers began his new job with the Premier League club at the weekend, and was not at home at the time.
"We don't have the references we have with other coaches and other teams, but the most important thing is to be concentrated on ourselves and on our work".
Speaking to shamed pundits Richard Keys and Andy Gray as a guest pundit, former Manchester United and Chelsea manager Mourinho said that Rodgers should have waited until the end of the season before choosing to join the Foxes. The Celtic defender has a long way to go on his contract and unlike Brendan, young Kieran is Celtic through and through.